Methodology: The Analysis of Valuation

Josh Lerner

Empirical Methods in Corporate Finance

An alternative approach

Much of empirical corporate finance has examined changes in valuation:– Presumption of efficiency short-run event

studies.– Search for anomalies has relied on long-run

studies, despite:• Lack of theoretical foundations.

• Benchmarking issues.

• Problematic statistical properties.

An alternative approach (2)

Look at level of valuation, typically around financing events:– Is price “right”?– What affects prices?

Can borrow from substantial economic literature:– “Hedonic” pricing.– Price indices.

Long history in finance literature

Tests of dividend discount and other valuation models.

Analyses of information content of accounting earnings.

But generally limited understanding of the econometric issues explored in economics literature.

Growing sophistication

Continuing work in economics since Waugh’s [1928] pioneering study.

Growing awareness of estimation issues, interpretative challenges.

Development of approaches to address these issues.

Key elements

Criteria for selecting observations. “Market” valuation of firms. Data that should be correlated with market

value:– Profitability.– Sales.– Information on similar firms.

Econometric specification for estimation.

The Valuation of Cash Flow Forecasts: An Empirical Analysis

Kaplan and Ruback [JF, 1995].

Motivation

Seeks to assess which broad valuation methodologies work best:– Adjusted present value vs. comparables.

Also seeks to choose best tactics:– Different betas.– Different equity premia.– Different terminal growth rates.– Different comparable sources.

Overview

Examines 51 buyouts and recapitalizations in 1980s with detailed projections at time of deal.

Compares actual transaction valuations with forecasted value.

Formally and informally tests accuracy of valuation forecasts with different methods.

The Sample

124 MBOs and 12 recapitalizations, 1980-1989.

~40% have at least four years of projections (some only on pre-tax basis):– From “fairness opinion” at time of transaction,

which is often filed with SEC.

Data on comparable Compustat firms and other LBOs.

Computing Market Value

Assume market value=future cash flows + excess cash:– Value of common stock at closing.– Plus value of preferred stock at closing.– Plus book value of debt.– Plus transaction fees.– Less cash and marketable securities.

Computing Predicted Value

Compute sum of cash flows to all capital:– Net income.– Plus depreciation and amortization.– Less change in net working capital.– Less capital expenditures.– Plus interest.– Plus cash from asset sales (after tax).

Computing Predicted Value (2)

Compute terminal value:– Equate CapEx and D&A.

– Assume profitability will continue indefinitely.

– Grow at various rates.

Discount all at cost of unlevered equity:• Using CAPM and firm data.

• Using CAPM value-weighted portfolio of NYSE/AMEX firms in same industry.

• Using beta of market as a whole.

Computing Predicted Value (3)

APV argues should discount tax shield from interest at lower rate (cost of debt):– It is significantly less risky!

For comparables, look at ratio of value to EBITDA for:– All firms in same four-digit SIC & >$40 million

market capitalization.– All LBOs within same year.– All LBOs in same year and two-digit industry.

Comparing Market and Predicted Value Compute logarithm of ratio of predicted to

market values. Examine extent within 15% and size of

errors. Best performance by:

– APV-based methods.– Historical equity premium (7.4%).– 4% terminal growth rate.

Comparing Market and Predicted Value (2) Hard to assess relative performance:

– Tests are not nested.– Statistical properties of valuation ratio is not

well-defined.

Compare to errors in the pricing of. other securities

But are the differences significant?

Regression Analyses

Regress log of market value on log of predicted value:– Hope to get coefficient of zero for constant, one for

slope.– APV approaches give “better” answers.

• Would like to see formal hypothesis testing.

– Multiples analysis is less clean-cut.

When include multiple measures, both valuation approaches are significant.

Addressing Exogeneity

Are cash flows really unbiased expectations?– Could they be “reverse engineered” to generate

predicted values?

Address by looking at ex post accuracy of predictions:– Some evidence of bias in cash flow numbers:

• But U.S. entered recession in 1990.

– No significant pattern in EBITDA/sales ratios.

Addressing Exogeneity (2)

Also segmented into where “gaming” may be more or less of a problem:– Little difference in highly levered and less

levered transactions.

Argue that APV also provides good results in eight reverse LBOs, where projections are not public disseminated:– But “road show” presentations.

Other Issues

Do the market valuations capture everything?– Debt covenants.– Contingencies in purchase price.

Do other factors affect the price paid?– Kaplan-Stein [1993] on the rise of valuations in

1980s.

How endogenous is the filing of projections?

Take-Aways

Interesting effort to seriously address the determinants of firm value.

Great experimental setting for looking at these issues, despite remaining difficulties.

Refinements in testing are clearly possible.

Money Chasing Deals? The Impact of Fund Inflows on Private Equity Valuations

Gompers and Lerner [JFE, 2000]

Growing Interest in Institutions and Asset Pricing Earlier studies:

– Why do valuations of a single company differ in two countries’ exchanges?

– Why do valuations of closed-end funds differ from the securities that they hold?

– How do trades by institutional investors affect stock prices?

– How does long-run performance of IPOs relate to presence of institutional investors?

U.S. private equity is attractive arena.

Venture Capital Raised by Year

0

1000

2000

3000

4000

5000

6000

1969 1972 1975 1978 1981 1984 1987 1990 1993 1996

Mil

lio

ns

of

1994

Do

llar

s

Implications of Fund Inflows

Accounts of capital inflows affecting prices, or “money chasing deals.”

Several periods of apparently severe over-valuation, followed by low returns.

May affect allocation of capital across firms and direction of innovation.

Few Earlier Examinations

Imbalance in amount of work on asset pricing in public and private markets.

Kaplan and Stein look at 124 leveraged buyouts of public firms in 1980s:– Increased pricing mirrored market moves.– But rising premiums.

Also work on impact of capital inflows into developing country markets.

Contrasts Two Views of Price Movements Hypothesis 1: Rational asset pricing

– Prices should reflect expected discounted future cash flows of firms.

– Sufficient substitutes exist for each firm, so shifts in supply of funds should not matter.

– Correlations with public market values in same industry, firm characteristics, etc.

Contrasts Two Views of Price Movements (2) Hypothesis 2: Market frictions

– May be relatively limited number of attractive firms or entrepreneurs.

– Inflows of funds may lead to more competition between VCs and higher prices.

– May have disproportionate effects on certain market segments.

The Data Set

VentureOne:– Established in 1987.– Collects profiles on venture-backed firms from firms

and VCs on monthly basis.– Collects data on firms (e.g., industry, employment,

sales), and financings (investors, amount, valuation).– Incentives for cooperation.

• Valuation data in 55% of 7375 rounds, 1987-1995, or 4069 transactions.

Data Supplements

Missing start dates and industries. Older employment and sales data. Inflation-adjusted flow into venture and

buyout funds by quarter. Public market returns and accounting data

from CRSP and Compustat for all firms in each of 35 three-digit industries.

Measures of Market Value

For each of 35 three-digit industries:– Equal- and value-weighted monthly indexes

from 1987 to 1995 with monthly rebalancing.– Unweighted and weighted ratio of net income

in previous four quarters to equity market value at quarter’s beginning (E/P).

– Unweighted and weighted ratio of equity book value to equity market value at quarter’s beginning (B/M).

Econometric Methodology

“Pre-money” valuations. “Log-log” specifications. Independent variables: firm’s industry, stage,

location, and age; industry market value; and VC inflows in past four quarters.

Employment, sales, or full sample. Controls for small-cap stocks, later rounds,

etc.

Econometric Methodology (2)

Many firms have multiple financings from VCs.

Dependent variable: difference in logarithm of valuations.

Independent variable: differences in the same variables used before.

Econometric Methodology (3)

Will the sensitivity of pricing to VC fund inflows or public market movements vary with:– stage of investment?– location of investment? – inflows into particular sector?

Econometric Methodology (4)

Ultimate outcomes:– Do shifts in inflows and pricing reflect changes

in deal quality?– If inflows change in response to deal quality,

and rate of investment adjusts more slowly, then quality will vary.

– Look at probability of successful exit.

Take-Aways

Apparent evidence of impact of inflows on valuations:– Doubling of inflows into VC funds leads to 7%

to 22% increase in valuations.

Address causation concerns in a variety of ways.

Remaining interpretative issues.

“Empirical Testing of Real Option-Pricing Models”

Quigg

JF, 1993

Attempts to seriously test “real options” Focuses on real estate. Seek to understand how much option to

wait to develop adds to property value. Compares with large sample of actual

transaction prices.

Formal model

Building prices follow an observable, stochastic process.

Developer can choose to continue to hold undeveloped land, or construct project:– Based on Titman [1985] and Williams [1991].

The sample

3200 transactions involving developed parcels, 1976-1979:– Will use to estimate ultimate potential for each parcel.

Estimates on cost of development of buildings of different types.

2700 transactions involving unimproved parcels. Urban setting biases against results.

First step

Estimate hedonic regression using developed parcels:– Separate regressions by year and zoning class.

Regress logarithm of price on:• Log of square footage.

• Log of lot size.

• Log of height.

• Log of age.

• Dummies for region and quarter.

Second step

Generated predicted building values for undeveloped sites:– Use coefficients from hedonic regression.– Predict height using average height.– Choose size that maximizes revenues, conditional on

attributes.

Potential biases from underestimating newness, expected supply shifts, or not controlling for properties that don’t sell.

Third step

Generate expected values using option pricing model:– Sensitivity to pay-out rate from undeveloped

property.– Sensitivity to economies of scale with size:

• Will impact how large buildings developed.

Compute “intrinsic value” (case when =0, or immediate development).

Testing the results

Compare predicted variance of developed properties to published estimates:– Range of 19% to 28%.– Studies of repeat housing sales imply valuations of

15%. Compare valuation implied by option pricing

to immediate development:– Difference averages 6%:

• Greatest in industrial.– May reflect data issues.

• Even without industrial properties, about 5% premium.

Testing the results (2)

Regress market price (per square foot) on predicted value:– Neither model stands out.

– Reject joint hypothesis that slope 1 and intercept 0 (errors in variables?).

– Then use both intrinsic price and option premium as independent variables:

• Constant falls.

• Both coefficients closer to one.

• But added explanatory power low.

Wrap-up

Serious attempt to test these ideas. Choosing a study site where:

– Tractable theoretical framework.– Sufficient data availability.

Hedonic analysis critical input into the process.

More General Methodological Issues Heteroskedasticity:

– Variance of estimates may differ due to differ to:• Volatility of market conditions.• Complexity of transactions.• Number of observations.

– To address concern, may:• Weight by estimate of variance (as in event study

approach).• Allow variance to vary across groups [White, 1980].

More General Methodological Issues (2) Choice of specification:

– Log, semi-log, and level are three common representations.

– More complex structures also seen.

To address concern, may:– Choose one approach [Gompers-Lerner].– Try alternative methods [Kaplan-Ruback].– Formally test through a Box-Cox [1964]

specification.

More General Methodological Issues (3) Omitted variable bias:

– Variables may be highly significant because correlated with other (missing) measures:

• Weight in automobile pricing.

– May lead to problematic interpretations:• May conclude that variable itself is important, when

actually correlated measure is.

Addressing omitted variable bias

Add wide variety of control variables to limit possibility.

Use instrumental variable for key variables to reduce correlation.

Look at ex post outcome to limit assure that no correlation.

More General Methodological Issues (4) Autocorrelation of residuals:

– Observations may not be independent due to industry, timing clustering.

– May depress standard errors.

If problem is multiple observations of same firm, can address:– Gompers and Lerner employ GLS specification that

allows autocorrelation in residuals.

More difficult if correlation across firms.

Open Issue

Much of pricing research in recent years has focused on simultaneous estimation:– Hedonic approach only really “works” if:

• Supply of characteristic is fixed: coefficients reflect consumer valuations.

• Supply curve is flat (perfect competition): coefficients reflect cost of production.

– Otherwise, need to map out both demand and supply curves:

• Barry and Pakes have focused on this question.

Open Issue (2)

Papers considered today fully grapple with this issue:– Kaplan-Ruback do not really address.– Otgher twor assume demand shift but flat

supply:• Reality likely to be more complex.

Conclusions

Older finance literature and very recent work.

Innovations in economic methodology in this area.

Tool may allow to address a variety of interesting questions.